Signatures for shape coexistence and shape/phase transitions in even–even nuclei

Abstract

Systematics of B(E2) transition rates connecting the first excited $0_2^+$ state to the first excited $2_1^+$ state of the ground state band in even-even nuclei indicates that shape coexistence of the ground state band and the first excited $K=0$ band should be expected in nuclei lying within the stripes of nucleon numbers 7-8, 17-20, 34-40, 59-70, 96-112 predicted by the dual shell mechanism of the proxy-SU(3) model, avoiding their junctions, within which high deformation is expected. Systematics of the excitation energies of the $0_2^+$ states in even-even nuclei show that shape coexistence due to proton-induced neutron particle-hole excitations is related to a first order shape/phase transition from spherical to deformed shapes, while shape coexistence due to neutron-induced proton particle-hole excitations is observed along major proton shell closures.

Prolate-oblate shape transitions and O(6) symmetry in even–even nuclei: a theoretical overview

“…A by-product of proxy-SU(3) symmetry and the dominance of the highest weight irreps is the resolution [60,104,191,199] of the long standing problem of the dominance of prolate over oblate shapes [17,18] in the ground states of even-even nuclei. Another by-product of the proxy-SU(3) symmetry is the dual shell mechanism [200], which predicts that shape coexistence can occur only on specific islands of the nuclear chart [77,201,202], recently corroborated through CDFT calculations [203,204].…”

“…Shape coexistence (SC) [77,[160][161][162]235] in even-even nuclei refers to the situation in which the ground state band and another K = 0 band lie close in energy but possess radically different structures, for example one of them being spherical and the other one deformed, or both of them being deformed, but one of them having a prolate shape and the other one exhibiting an oblate shape. A dual shell mechanism [202,236] proposed within the proxy-SU(3) scheme [59][60][61] suggests that SC can occur only within certain stripes of the nuclear chart, forming islands of SC, for the borders of which empirical rules have been recently suggested [201]. It is interesting to see where the lines along which a prolate to oblate transition is expected are lying in relation to the islands of SC, depicted in figure 1 of [77].…”

Shapes and structure for the lowest states of the 42,44Ca isotopes

“…The shape coexistence is not only a specific property of the even-mass nuclei [9], but is also met in odd-mass nuclei [8]. Recently, a proxy-SU(3) model [11][12][13] has been used for a better localization of these regions, conventionally called islands of shape coexistence [14,15]. Algebraic approaches, as the Interacting Boson Model (IBM) [16][17][18][19] and the Partial Dynamical Symmetry (PDS) [20], proved to be also appropriate tools in addressing this behavior in nuclei [21][22][23][24][25], especially in heavy mass region where the dimension of the SM configuration space is prohibitive.…”

“…The same approaches are also applied here for 42,44 Ca nuclei which are expected to present a spherical shape for the lowest states of the ground band, respectively deformed shapes for the states build on the top of the first excited 0 + state [62,63]. These isotopes are also good candidates for the presence of the coexistence phenomenon, according to some certain signatures as the low energy of the first excited 0 + state, large monopole transition between this state and ground state, respectively large quadrupole transitions (E2) between states from different bands [15,64,65]. As theoretical tools, the Bohr Hamiltonian with a sextic potential will be used for the description of the low-lying energy states and the associated shape dynamics, while the CDFT with DD-ME2 will be used to ascertain the ground state deformation properties of the considered nuclei and their suitability for the collective model treatment [32,33].…”